Municipal Water Pressure-Head Drop with Flow Rate: Location: Antigonish Municipality: Keating Court Date: August 14, 2009 ------------------------------------------------------------- Hose: Straight and level 60' length 5/8" ID (1.588e-3 m) open-ended to atmosphere Flow rate measured at open end of hose: 0.283 litre/sec or 17 litre/min or 2.83E-4 m^3/sec (23.7 sec to fill 6.7 litre container) Water Viscosity: 1.14e-3 N-sec Water Density: 1000 kg/m^3

Calculated Pressure-Head Drop due to Viscous Flow: ---------------------------------------------------------------- Using the measured flow rate above and hose diameter, we calculate: Vav = 1.43 m/sec (mean water flow velocity in hose) Reynolds # 19,890 (turbulent flow) Friction factor: 0.0266 (turbulent flow, with smooth inner surface of hose) Using the D'Arcy Weisbach expression for head loss along this hose: Head-loss per meter: 0.174 meter/meter Pressure-head loss per meter: 1710 Pa/meter (0.248 psi./meter) Therefore, for 60' (18.3 m) length of open-ended 5/8" ID hose, at this measured flow rate, we expect a pressure-head loss of about 4.5 psi along the hose. With the uniform hose with open-ended output at atmospheric pressure, the pressure measured at input to hose at tap is therefore expected to be 4.5 psi gauge, neglecting any other head-loss effects such as pressure-gauge configuration loss, hose-end irregularity etc. Pressure Measurement: ------------------------------ Pressure Gauge: Winters PEM 213 (0 - 60 psi FS range) Using a Y coupler to insert a water-pressure gauge at the tap, but WITHOUT water flowing: P(static) = 54 psi (+/- 3%) (static pressure head)

With the tap fully open and water flowing at the measured rate through the 60' open-ended hose: P(flowing) ~ 4.5 psi (+/- 10%) which is in close agreement with calculation above.

The total head at the tap outlet WITH WATER FLOWING is therefore: TPHF == Total pressure head at tap (with water flowing) = P(flowing) + 1/2*rho*Vav^2 where rho is density of water (1000 kg/m^3) and Vav is the average flow velocity (here 1.43 m/sec): TPHF = 4.5 psi + 0.15 psi = 4.65 psi. Compared to the STATIC pressure head at tap (no water flowing) of 54 psi, we conclude that the pressure head loss FROM THE CITY SUPPLY TO HOUSE OUTLET with this hose connected and with this flow rate (17 litre/min) is large at about 49 psi. What If .. -------------- If the city supply/infrastructure COULD maintain a pressure of say 40 psi at tap for this hose configuration with water flowing, what would be the expected flow rate? mean velocity? Reynolds number?: In this case, the Pressure Head Loss along the hose would be (40psi)/18.3 m = 2.19 psi/meter. Solving D'Arcy Weisbach viscous flow we find a flow rate of about 3.5 times higher than above: Flow Rate: 1 litre/sec (60 litre/min) Vav: 5.05 m/sec Reynolds # 70,350 Friction factor: 0.019